力學(xué)大會2015集資助批準(zhǔn)號點基金項目

屬力能裂性不斷已成設(shè)于進(jìn)破性樣驗前然以過視超聲渦等損結(jié)異或部陷行查但以接量地評材的學(xué)能的程度更以測備剩余因此對役源備力性進(jìn)測值樣儀ismtdidtin）別觀壓變形材損傷導(dǎo)測的性量著入度增而小于發(fā)們出一種壓韌應(yīng)然而經(jīng)的傷性論為以縮剪變?yōu)榈娜胄尾徊膫蛴斜貜睦韺τ萌敕繉倭狭研砸坏睦磉M(jìn)檢驗據(jù)的結(jié)典的uo-vrad-elan變形的孔洞萌生比孔洞變形對損傷的貢獻(xiàn)更大。由于損傷塑形力學(xué)參數(shù)與斷裂力學(xué)參數(shù)之間尚未建立明確的對應(yīng)關(guān)系，有必要對基于壓入損傷計算被測材料斷裂韌性這一工程上非常有的 Theinstrumentedindentationtechniquehaswellbeendevelopedtocharacterizetheelasticpropertiesofductilemetallicmaterials.Atnano-/submicro-scale,elasticmoduliinsensitivetotheindentationdepthcanbereliablyobtainedfromtheinitialslopeoftheindentationunloadingcurvebyproperlyconsideringthecorrectionfactorssuchasthe‘pile-up’or‘sink-in’effect[1].However,atmicro-/macro-scale,degradationoftheelasticpropertieshasbeenfrequentlyreportedandintermsofthedecaycurveoftheinferredelasticmodulus,anattractiveindentationtechniquehasbeenproposedtoestimatethefracturetoughnessofductilematerialsinaautomaticnon-destructiveway[2-4].Consideringindentationdoesnotinduceapparentcrackinginductilematerials(thisisdifferentfromtheindentationofbrittlematerialswherewell-definedcrackscanbeinducedandthefracturetoughnesscanbecalculatedbyusingsimplerelationships[5]),themechanismfortheindentation-inducedductiledamageandthevalidityofthedamage-basedindentationtechniqueforestimatingthefracturepropertiesneedfurtherinvestigations.Fromamicroscopicpointofview,thedamageandfailureofmanymetallicmaterialsoccursafterthenucleation,growthandcoalescenceofmicro-voids.Inordertodescribethisdamageandfractureprocess,severalmicro-mechanicalmodelsusinglocalapproacheshavebeenproposedamongwhichtheGurson-Tvergaard-Needleman(GTN)model[6,7]isthemostwidelyused.ThesingledamageparameterintheoriginalGTNmodelisthevoidvolumefractionofwhichtheevolutionischaracterizedbythenucleationofnewvoidsandgrowthofexisting

wherefisthevoidvolumefraction,f

andandf

representthenucleationandgrowthofvoids.Thegrowthofvoidscanbecorrelatedwiththerateofvolumechangewiththeassumptionthatthematrixmaterialisstically Anormaldistributionofvoidnucleationwithrespecttothesticstrainofthematrixmaterialisproposed 1εpε exp N SSN

1）Theprojectwassupportedby Mwhereεpistheequivalent sticstrainofthematrixmaterial,SNandεNarethestandarddeviationandthemeanvalueofthedistributionofthe sticstrain,FNisthetotalvoidvolumefractionthatcanbeMWithanassumptionthattheisolatedsphericalvoidsareuniformlydistributedinacontinuumtheyieldfunctionoftheGTNmodelhasthefollowing σq2 3qσ 2 ,f, cosh 2m q1 2σwhereσmisthenormalmeanstress,qistheconventionalvonMisesequivalentstress,σistheπstressofthematrixmaterial,andq1,q2arefittingparameters.BasedontheπD f2 whereDisthedamagevariableandfisthevoidvolumefraction.ThedegradationofelasticityiscorrelatedwiththedamagevariablethroughE1DE0whereE0istheelasticmodulusoftheundamagedmaterial.TheoreticalWithinrangeofhighlevelsofstresstriaxialitieswheresphericalvoidgrowthisthepredominantmechanism,theGTNmodelhasverygoodperformance.However,undersheardominateddeformation,wherefailureismainlydrivenbytheshearlocalization[8],themodeldoesnotperformwell.Inpractice,thevoidvolumefractionisnotallowedtoinitiateorgrowundernegativestresstriaxialitiesinthefiniteelementimplementationoftheclassicalGTNmodel[9,10].Asaconsequence,theductiledamageinducedbyindentationcannotbecapturedbytheclassicalGTNmodelatall.Althoughexperimentalevidenceforthesusceptibilitytoshearfractureunderloworevennegativetriaxialityhasbeenreportedbymanyresearchers[11-13],knowledgeoftheunderlyingmechanismsisstilllimited.NahshonandHutchinson[14]attributedtheshearsofteningtovoiddistortionandthesofteningmechanismisphenomenologicallyrepresentedbyequivalentgrowthofvoids,i.e., 27J2v1fpkf1 3 v

2q3wherethesecondtermontheright-handsideofEq.(6)representstheshearsofteningduetovoiddistortion,kisascalingfactor,J3isthethirdinvariantofthedeviatoricstressandPis sticrate.ThemodifiedGTNmodelwithNahshonandHutchinson’sextensionhasbeenimplementedwithintheframeworkofthegeneral-purposefiniteelementsolver,i.e.,ABAQUS,bywritingtheuser-definedsubroutine,i.e.,UMAT.Ageneralizedmid-pointalgorithm[9]wasadoptedtoupdatethestress.Anaxisymmetricfiniteelementmodelwasbuiltuptostudythedegradationoftheelasticityofanaluminumalloyinducedbysphericalindentations.ItisfoundthatthemodifiedGTNmodelwithNahshonandHutchinson’sextensioncanonlyqualitativelypredictthedegradationoftheinferredelasticmodulus(Fig.1).Thelowdecayrateofthepredictedelasticmodulusimpliestheevolutionofdamageisunderestimatedbythemodifiedmodel.Consideringvoiddistortiondoesnotchangethevoidvolumefractionandtherefore,theshearsofteningshouldbetreatedseperay,Xue[15]proposedanindependentdamagevariablewhichisdrivenbytheshearstrainandscaledbythevoidvolumefraction[15],shear

q3fq4

shear

isthedamagerate,q3andq4arematerialconstants,εistheequivalentstrain.TheofthethirdstressinvariantwasdepictedinaphenomenologicalwaybyaLodeangledependencefunction,i.e.,gθ[15].Xue’sextensionhasbeenincorporatedintotheGTNmodelbyusingtheUMATsubroutineandfiniteelementsimulationswereconductedtostudythedegradationoftheelasticityofthealuminumalloyinducedbysphericalindentations.Asimilarunderestimationofthedecayrateofthepredictedelasticmoduluswasobservedandthissuggeststhattheshear–drivendamageiseithernotfullydescribedbyXue’sextension.OtherinvestigationsalsofindthatalthoughtheresultsobtainedwiththeabovemodifiedGTNmodelsshowimprovementsinthepredictionofdamage,bothmodelshaveinherentlimitationsandthepredictionofthelocationoffracture,thediscementtofractureandtheequivalentsticstraintofracture,forcombinedstressstates,isnotadequate[8,16,17].Thesefindingsindicatethatothermechanismforshearsofteningmayexist.BothNahshonandHutchinson’sandXue’sextensionsarebasedontheassumptionthatsheardeformationdoesnotinitiatenewvoidsandtheshearsofteningisonlyattributedtothedistortionofexistingvoids.Infact,engineeringalloysloadedundershearconditionsmaycreatelocalizationbandsduetothenucleationofsecondaryvoidsthroughavoidsheetingmechanismduetosecond-phaseparticledeboningandcracking[8].By ogywiththenucleationmechanismofvoidsdrivenbysticstrainorhydrostaticpressure,anindependentnucleationmechanismthattriggersvoidsheetingandlocalizationwasproposed

1εpε2 N N

2

shear

isthenucleationrateofdamage,DNrepresentsthefractionofallsecond-phasedeviation,εpistheequivalent sticstrain.Thedamagenucleationmodel,i.e.,Eq.(6),aswellasthedamageevolutionmodel,i.e.,Eq.(5),havebeenincorporatedintotheGTNmodelbyusingtheUMATsubroutine.Itisfoundthattheexperimentalmeasurementcanbewellreproducedbythefiniteelementsimulations(Fig.1).Tofurtherverifythedamagenucleationmechanism,theindentation-induceddegradationofelasticityoffourtypesofsteelswassimulatedbyusingfiniteelementcalculations.TheexperimentalmeasurementsarereportedinRef.[2].Boththeupperlimitandthelowlimitofthedecayratecanbetativelypredicted(Fig.2).ExperimentalUpperExperimentalUpperlimitpredictedbyGTNmodelwithNahshonandHutchinson'sextensionLowerlimitpredictedbyGTNmodelwithNahshonandHutchinson'sextensionPredictionbyGTNmodelwithXue'sextensionandthedamagenucleationmechanicsmSA335P12UpperlimitpredictionbyGTNmodelXue'sextensionandthedamagenucleationmechanicsmLowerlimitpredictionbyGTNmodelwithXue'sextensionandthedamagenucleationReducedReduced umindentationFigure1Degradationofelasticstiffnessofan

umindentationFigure2Degradationofelasticstiffnessoffourtypesofloads.BothNahshonandHutchinson’sandXue’sextensionneglectthedamagenucleationmechanismandassumethattheshearsofteningisonlyattributedtothedistortionofexistingvoidswhichisscaledbyafactordependingonthethirdstressinvariant.Therefore,theshearsofteningeffectisnotableonlyinanarrowloads.BothNahshonandHutchinson’sandXue’sextensionneglectthedamagenucleationmechanismandassumethattheshearsofteningisonlyattributedtothedistortionofexistingvoidswhichisscaledbyafactordependingonthethirdstressinvariant.Therefore,theshearsofteningeffectisnotableonlyinanarrowrangebeneaththeindenter(Fig.3(a)).Thedamagenucleationmodeli.e.,Eq.(6),assumesthatnewdamagecanbeeparticlesandinawidermSEMonandFigure3Predicteddamagecontourwithout(a)andwith(b)consideringthedamagenucleationmechanismbyDiscussionandConsideringfractureanddamagecanbecorrelatedtoeachotheronthebasisofanenergyequivalence[18],itmaybefeasibletoinferthefracturepropertiesofductilematerialsfromtheindentation-induceddamageifthedamageisadequaydevelopedandthecorrelationbetweenfractureanddamagehasbeenestablished.Sincethedamageofengineeringalloysoccursonalengthscaleofmicro-meter(theaveragesizeofthesecondphaseparticles)[19],adeepmicro-indentationoramacro-indentationismorefavorabletoinduceobservabledamage.Althoughprogresshasbeenmadetowardcorrelatingthefracturebehaviorandthedamagebehaviorofbrittlematerials[18],itisstillratherchallengingtoestablishsuchrelationshipsforductilematerials.Forexample,itisfoundthatthevolumefractionofvoidsisnotsufficienttodescribetheinitiationoffracture[9,15].Thisfindingunderminesthetheoreticalbasisofthedamage-basedindentationtechniqueforestimatingthefracturepropertiesofductilematerialsandmayexinwhyanon-uniquecriticalvoidvolumefractionisusedbythetechnique[2,20].Furthertheoreticalinvestigationsareneededbeforethetechniqueisappliedasanalternativetotheconventionalfracturetoughnesstesting.Insummary,micro-andmacro-indentationcaninducenotabledegradationofelasticstiffnessofductilealloysasaconsequenceoftheshear-drivendamage.Bycomparingthepredicteddegradationwiththatmeasuredbyindentationtesting,itisfoundthatthedamageduetothedistortionofexistingvoidsisnotenoughandthenucleationofnewsecondaryvoidsthroughthevoidsheetingmechanismmakesanimportantcontributiontotheoverallshear-drivendamage.Consideringthecorrelationbetweenthefracturebehaviorandthedamagebehaviorofductilematerialsisyettobeestablished,thedamage-basedindentationtechniqueforestimatingthefracturepropertiesofductilematerial,althoughveryattractiveinpracticalapplicationsandseemingtobeeffectiveinsomeapplications,needsfurthertheoreticalW.C.OliverandG.M.Pharr,J.Mater.Res.19(2004),J.S.Lee,J.i.Jiang,B.W.Lee,Y.Choi,S.G.LeeandD.Kwon,Acta.Mater.54(2006),J.Li,F.G.Li,M.He,F.M.Xue,M.J.ZhangandC.P.Wang,Mater.Design40(2012),S.Amiri,N.Lecis,A.ManesandM.Giglio,Mech.Res.Commun.58(2014),B.R.LawnandE.R.Fuller,J.Mater.Sci.10(1976),A.L.Gurson,ASMEJ.Eng.Mater.Technol.99(1977),V.TvergaardandA.Needleman,Acta.Metall.32(1984),L.Malcher,F.M.AndradePiresandJ.M.A.CésardeSá,Int. s.54(2014),Z.L.Zhang,C.ThaulowandJ.?deg?rd,Eng.Frac.Mech.67(2000),ABAQUSTheoryManual,Version6.13,DassaultSystèmes,F.A.McClintock, sticityaspectsoffracture.In:Leibowitz,H.(Ed.),Fracture,vol.3.AcademicPress,1971.Y.BaoandT.Wierzbicki,Int.J.Mech.Sci.46(2004),I.BarsoumandJ.Faleskog,Int.J.SolidsStructures44(2007),K.NahshonandJ.Hutchinson,Eur.J.Mech.A/So